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Match List-I with List-II

List-IList-II
Matrix A∣adj A∣2\left\vert \text{adj } A \right\vert^2
(A) [3728]\begin{bmatrix} 3 & 7 \\ 2 & 8 \end{bmatrix}(I) 121121
(B) [5−124]\begin{bmatrix} 5 & -1 \\ 2 & 4 \end{bmatrix}(II) 144144
(C) [36514]\begin{bmatrix} 3 & 6 \\ 5 & 14 \end{bmatrix}(III) 484484
(D) [7523]\begin{bmatrix} 7 & 5 \\ 2 & 3 \end{bmatrix}(IV) 100100

Choose the correct answer from the options given below:

Solution

✅ Correct Option: 3

For a 2×22\times2 matrix, ∣adjA∣=∣A∣|adj A|=|A|, so ∣adjA∣2=∣A∣2|adj A|^2=|A|^2.

(A) ∣A∣=24−14=10⇒100|A|=24-14=10\Rightarrow100, so (IV).

(B) ∣A∣=20+2=22⇒484|A|=20+2=22\Rightarrow484, so (III).

(C) ∣A∣=42−30=12⇒144|A|=42-30=12\Rightarrow144, so (II).

(D) ∣A∣=21−10=11⇒121|A|=21-10=11\Rightarrow121, so (I).

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